Quantile Function
Lognormal distribution quantile function.
The quantile function for a lognormal random variable is
for 0 <= p < 1
, where mu
is the location parameter and sigma > 0
is the scale parameter.
Usage
var quantile = require( '@stdlib/stats/base/dists/lognormal/quantile' );
quantile( p, mu, sigma )
Evaluates the quantile function for a lognormal distribution with parameters mu
(location parameter) and sigma
(scale parameter).
var y = quantile( 0.5, 0.0, 1.0 );
// returns 1.0
y = quantile( 0.5, 4.0, 1.0 );
// returns ~54.598
y = quantile( 0.8, 4.0, 1.0 );
// returns ~126.675
y = quantile( 0.8, 4.0, 4.0 );
// returns ~1582.063
If provided a probability p
outside the interval [0,1]
, the function returns NaN
.
var y = quantile( 1.9, 0.0, 1.0 );
// returns NaN
y = quantile( -0.1, 0.0, 1.0 );
// returns NaN
If provided NaN
as any argument, the function returns NaN
.
var y = quantile( NaN, 0.0, 1.0 );
// returns NaN
y = quantile( 0.0, NaN, 1.0 );
// returns NaN
y = quantile( 0.0, 0.0, NaN );
// returns NaN
If provided sigma <= 0
, the function returns NaN
.
var y = quantile( 0.4, 0.0, -1.0 );
// returns NaN
y = quantile( 0.4, 0.0, 0.0 );
// returns NaN
quantile.factory( mu, sigma )
Returns a function for evaluating the quantile function of a lognormal distribution with parameters mu
and sigma
.
var myquantile = quantile.factory( 4.0, 2.0 );
var y = myquantile( 0.2 );
// returns ~10.143
y = myquantile( 0.8 );
// returns ~293.901
Examples
var randu = require( '@stdlib/random/base/randu' );
var quantile = require( '@stdlib/stats/base/dists/lognormal/quantile' );
var sigma;
var mu;
var p;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
p = randu();
mu = (randu() * 10.0) - 5.0;
sigma = randu() * 20.0;
y = quantile( p, mu, sigma );
console.log( 'p: %d, µ: %d, σ: %d, Q(p;µ,σ): %d', p.toFixed( 4 ), mu.toFixed( 4 ), sigma.toFixed( 4 ), y.toFixed( 4 ) );
}